Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

269×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize10.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (* x.im y.re) (* x.re y.im))
24.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series120.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (* x.im y.re) (* x.re y.im))
80.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify104.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421

prune152.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
1.4b	(- (* x.im y.re) (* x.re y.im))
15.6b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 110

Calls

3 calls:

24.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series337.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	537	1095
1	2236	907
2	5002	905

prune269.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
1.4b	(- (* x.im y.re) (* x.re y.im))
15.6b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log`
17×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-exp`
7×	`cbrt-undiv`
5×	`add-log-exp`
4×	`prod-exp` `associate-/r*` `div-inv`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 99

Calls

3 calls:

10.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series268.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
36.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	423	962
1	1691	852
2	5001	851

prune276.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.2b	(/ 1 (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
1.4b	(- (* x.im y.re) (* x.re y.im))
15.6b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`associate-/r*`
32×	`add-exp-log`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
2×	`flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `prod-diff` `inv-pow`

Counts

4 → 326

Calls

4 calls:

11.0ms	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
16.0ms	(/ 1 (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series426.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
183.0ms	(/ 1 (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))))
39.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify66.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1092	4970
1	5002	4493

prune752.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes413.0ms

Accuracy

34.5% (8.2b remaining)

Error of 13.1b against oracle of 4.9b and baseline of 17.4b

bsearch174.0ms

Steps

Iters	Range		Point
9	9.327928414647935e+164	8.305481265032157e+173	5.214345045033657e+171
5	4.01184781369023e+154	1.0628363692372637e+155	4.0740961827290516e+154
10	6.4279230489962455e+31	5.831860694222546e+42	3.8584984167732284e+39
5	-2.3926456590010396e+94	-1.0396556759696811e+94	-1.928097023327238e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	32
1	47	32
2	47	32

end0.0ms

sample871.0ms

Algorithm

intervals

Results

648.0ms

8500×

body

valid